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/****************************************************************************
**
** Copyright (C) 1993-2009 NVIDIA Corporation.
** Copyright (C) 2017 The Qt Company Ltd.
** Contact: https://www.qt.io/licensing/
**
** This file is part of Qt 3D Studio.
**
** $QT_BEGIN_LICENSE:GPL$
** Commercial License Usage
** Licensees holding valid commercial Qt licenses may use this file in
** accordance with the commercial license agreement provided with the
** Software or, alternatively, in accordance with the terms contained in
** a written agreement between you and The Qt Company. For licensing terms
** and conditions see https://www.qt.io/terms-conditions. For further
** information use the contact form at https://www.qt.io/contact-us.
**
** GNU General Public License Usage
** Alternatively, this file may be used under the terms of the GNU
** General Public License version 3 or (at your option) any later version
** approved by the KDE Free Qt Foundation. The licenses are as published by
** the Free Software Foundation and appearing in the file LICENSE.GPL3
** included in the packaging of this file. Please review the following
** information to ensure the GNU General Public License requirements will
** be met: https://www.gnu.org/licenses/gpl-3.0.html.
**
** $QT_END_LICENSE$
**
****************************************************************************/
namespace Q3DStudio {
//==============================================================================
/**
* Generic Bezier parametric curve evaluation at a given parametric value.
* @param inP0 control point P0
* @param inP1 control point P1
* @param inP2 control point P2
* @param inP3 control point P3
* @param inS the variable
* @return the evaluated value on the bezier curve
*/
inline FLOAT EvaluateBezierCurve(FLOAT inP0, FLOAT inP1, FLOAT inP2, FLOAT inP3, const FLOAT inS)
{
// Using:
// Q(s) = Sum i=0 to 3 ( Pi * Bi,3(s))
// where:
// Pi is a control point and
// Bi,3 is a basis function such that:
//
// B0,3(s) = (1 - s)^3
// B1,3(s) = (3 * s) * (1 - s)^2
// B2,3(s) = (3 * s^2) * (1 - s)
// B3,3(s) = s^3
/* FLOAT theSSquared = inS * inS; //
t^2
FLOAT theSCubed = theSSquared * inS; //
t^3
FLOAT theSDifference = 1 - inS; // (1 -
t)
FLOAT theSDifferenceSquared = theSDifference * theSDifference; // (1 -
t)^2
FLOAT theSDifferenceCubed = theSDifferenceSquared * theSDifference; // (1 - t)^3
FLOAT theFirstTerm = theSDifferenceCubed; // (1 -
t)^3
FLOAT theSecondTerm = ( 3 * inS ) * theSDifferenceSquared; // (3 * t) * (1
- t)^2
FLOAT theThirdTerm = ( 3 * theSSquared ) * theSDifference; // (3 * t^2) *
(1 - t)
FLOAT theFourthTerm = theSCubed; //
t^3
// Q(t) = ( p0 * (1 - t)^3 ) + ( p1 * (3 * t) * (1 - t)^2 ) + ( p2 * (3 * t^2) * (1 - t)
) + ( p3 * t^3 )
return ( inP0 * theFirstTerm ) + ( inP1 * theSecondTerm ) + ( inP2 * theThirdTerm ) + (
inP3 * theFourthTerm );*/
FLOAT theFactor = inS * inS;
inP1 *= 3 * inS;
inP2 *= 3 * theFactor;
theFactor *= inS;
inP3 *= theFactor;
theFactor = 1 - inS;
inP2 *= theFactor;
theFactor *= 1 - inS;
inP1 *= theFactor;
theFactor *= 1 - inS;
inP0 *= theFactor;
return inP0 + inP1 + inP2 + inP3;
}
//==============================================================================
/**
* Inverse Bezier parametric curve evaluation to get parametric value for a given output.
* This is equal to finding the root(s) of the Bezier cubic equation.
* @param inP0 control point P0
* @param inP1 control point P1
* @param inP2 control point P2
* @param inP3 control point P3
* @param inX the variable
* @return the evaluated value
*/
inline FLOAT EvaluateInverseBezierCurve(const FLOAT inP0, const FLOAT inP1, const FLOAT inP2,
const FLOAT inP3, const FLOAT inX)
{
FLOAT theResult = 0;
// Using:
// Q(s) = Sum i=0 to 3 ( Pi * Bi,3(s))
// where:
// Pi is a control point and
// Bi,3 is a basis function such that:
//
// B0,3(s) = (1 - s)^3
// B1,3(s) = (3 * s) * (1 - s)^2
// B2,3(s) = (3 * s^2) * (1 - s)
// B3,3(s) = s^3
// The Bezier cubic equation:
// inX = inP0*(1-s)^3 + inP1*(3*s)*(1-s)^2 + inP2*(3*s^2)*(1-s) + inP3*s^3
// = s^3*( -inP0 + 3*inP1 - 3*inP2 +inP3 ) + s^2*( 3*inP0 - 6*inP1 + 3*inP2 ) + s*( -3*inP0
// + 3*inP1 ) + inP0
// For cubic eqn of the form: c[0] + c[1]*x + c[2]*x^2 + c[3]*x^3 = 0
FLOAT theConstants[4];
theConstants[0] = static_cast<FLOAT>(inP0 - inX);
theConstants[1] = static_cast<FLOAT>(-3 * inP0 + 3 * inP1);
theConstants[2] = static_cast<FLOAT>(3 * inP0 - 6 * inP1 + 3 * inP2);
theConstants[3] = static_cast<FLOAT>(-inP0 + 3 * inP1 - 3 * inP2 + inP3);
FLOAT theSolution[3] = { 0 };
if (theConstants[3] == 0) {
if (theConstants[2] == 0) {
if (theConstants[1] == 0)
theResult = 0;
else
theResult = -theConstants[0] / theConstants[1]; // linear
} else {
// quadratic
INT32 theNumRoots = CCubicRoots::SolveQuadric(theConstants, theSolution);
theResult = static_cast<FLOAT>(theSolution[theNumRoots / 2]);
}
} else {
INT32 theNumRoots = CCubicRoots::SolveCubic(theConstants, theSolution);
theResult = static_cast<FLOAT>(theSolution[theNumRoots / 3]);
}
return theResult;
}
inline FLOAT EvaluateBezierKeyframe(FLOAT inTime, FLOAT inTime1, FLOAT inValue1, FLOAT inC1Time,
FLOAT inC1Value, FLOAT inC2Time, FLOAT inC2Value, FLOAT inTime2,
FLOAT inValue2)
{
// The special case of C1Time=0 and C2Time=0 is used to indicate Studio-native animation.
// Studio uses a simplified version of the bezier animation where the time control points
// are equally spaced between the starting and ending times. This avoids calling the expensive
// InverseBezierCurve function to find the right 's' given 't'.
FLOAT theParameter;
if (inC1Time == 0 && inC2Time == 0) {
// Special case signaling that it's ok to treat time as "s"
// This is done by assuming that Key1Val,Key1C1,Key1C2,Key2Val (aka P0,P1,P2,P3)
// are evenly distributed over time.
theParameter = (inTime - inTime1) / (inTime2 - inTime1);
} else {
// Compute the "s" parameter on the Bezier given the time
theParameter = EvaluateInverseBezierCurve(inTime1, inC1Time, inC2Time, inTime2, inTime);
if (theParameter <= 0.0f)
return inValue1;
if (theParameter >= 1.0f)
return inValue2;
}
return EvaluateBezierCurve(inValue1, inC1Value, inC2Value, inValue2, theParameter);
}
}
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